Sharpening geometry
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 This topic has 6 replies, 5 voices, and was last updated 08/13/2018 at 11:59 am by wickededge.

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08/11/2018 at 12:46 pm #47225
Sharpening and a little geometry
Enclosed is a couple of graphs that some might find useful.
I have seen people propose measuring the sharpening angle by measuring the length of the bevel. The first graph you might find handy is to estimate the sharpening angle on an existing knife. Assuming you have a digital caliper or something similar, measure the thickness of the knife at the point of intersection of the bevel. Then measure the length of the bevel. This creates a triangle solved by this graph. Intersect those two values on the horizontal and vertical axis and that point will show you the sharpening angle. It is difficult to get an exact reading on the bevel angle but it’s a start.
We have all seen the sharpening angle change when the vertical location on a knife is different so we use the angle cube. The second graph shows the solution of this triangle created by the location of the ball joint and the height of the sharpening point above the ball joint. The distance from the center line of the rod to the abrasive is also taken into account. The graphs show the amount you move the ball joint horizontally after determining the height of knife. (Not the markings on the degree rod) This all starts with the knife being vertical in the clamp or that error must be added or subtracted to the angle measurements.
Comets, correction?
Richard
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08/11/2018 at 12:59 pm #47228Richard, this is a little difficult, at least for me, to conceptualize what you mean, from the words I’m reading. It would be much easier with a visual aide of a drawing labeled to show the points you reference for the measurements, a labeled knife for example.
Take a look at your axis labels on the graphs you attached. I believe the second is misslabeled/misspelled or I just don’t understand the nomenclature.
I’m not sure what you mean by “measure the thickness of the knife at the point of intersection of the bevel”. Is this the thickness of the knife blade at the shoulder, (i.e.,the lower margin of the bevel where it starts)?
Also, I don’t understand what you’re saying here: “We have all seen the sharpening angle change when the vertical location on a knife is different so we use the angle cube.” What vertical position? An imagined center line down through the apex and splitting the spine, perpendicular to the horizontal zeroed base? How can this vertical change? The vice is fixed in a stationary position and designed to clamp the knife repeatedly in the same position, (i.e, when using the Gen 3 Vice).
Marc
(MarcH's RackIts)08/11/2018 at 5:05 pm #47231I can’t tell if you are trying to determine the angles of the bevels with the method you described or if you are trying to measure the angle on the primary grind of the knife.
I say this as someone who enjoys mathematics (my minor in college), but I find that the fastest and most accurate way to determine the angle of the bevels on the knife is to put sharpie on the bevels and to do a few passes with a fine stone and adjust until the sharpie is completely removed.
08/12/2018 at 2:24 am #47242Actually, I find the graphs quite understandable, although Richard’s explanation might have been a little confusing to some.
The “bevel vs thickness” graph tells you what the angle is, for a given thickness at the shoulders of the bevels and a given width of the bevel. A little tricky getting an accurate reading on what could be a microscopic scale. I frequently sharpen knives with bevel width of less than half a millimeter. A very small change in bevel width could make a large angular change.
The “offset of the ball” graph tells you where to position the ball joint for a given angle and a given height of the edge. Perhaps this graph would be more readable if the left vertical axis were angle instead of ball joint position, which would be the right vertical axis. I tend to not read a graph expecting to find a function (answer) on the left vertical axis.
In either case, I don’t think the graphs have the level of precision we’d like. Another possible, but more useful variant would be to graph detent position as a function of desired angle and edge height. For example; you have a known height of the edge and you want to sharpen at 20 dps; the graph tells you to use detent position “x”. Likewise, the graph would tell you that detent position 23 at a given edge height would produce an angle “y.” This would help sharpeners who don’t have an angle cube. Of course, the position of the microadjust screws would “screw” with the numbers, but I suppose you could preset them to a fixed position.
08/12/2018 at 6:57 am #47243That explanation clarified it for me. Thanks TC!
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08/12/2018 at 8:48 am #47244I can present the data in many different formats and accuracy if you desired or if you think it worthwhile. It is all done in an excel spreadsheet and I would be happy to give you that or the equation as well.
Richard
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08/13/2018 at 11:59 am #47246I can present the data in many different formats and accuracy if you desired or if you think it worthwhile. It is all done in an excel spreadsheet and I would be happy to give you that or the equation as well. Richard
Richard,
Thank you for posting this, it’s awesome. I understand the charts very well and I think they could be useful to a lot of people because the answer two basic but important questions:
 How does the angle change with knives of different heights with the pivot set at various distances from the center line of the blade?
 How does the bevel width change with different blade thicknesses at various angles?
Clay

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